Problem: Simplify the expression. $ (3z^{5}-z^{4}+3z^{3}) + (-2z^{6}+z^{5} ) $
Answer: Since we are adding polynomials, we can simply remove the parentheses. $3z^{5}-z^{4}+3z^{3} - 2z^{6}+z^{5}$ Identify like terms. $ + \color{#DF0030}{3 z^5} - { z^4} + \color{#9D38BD}{3 z^3} - {2 z^6} + \color{#DF0030}{ z^5} $ Combine like terms. $ { -2 z^6} + \color{#DF0030}{ z^5} + { -1 z^4} + \color{#9D38BD}{ 3 z^3} $ Add the coefficients. $-2z^{6}+4z^{5}-z^{4}+3z^{3}$